# Experimental Investigation on the Vector Characteristics of Concentrated Solar Radiation Flux Map

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Details

#### 2.1. Experimental Method

^{2}. The symbol GV is the gray value of the CCD camera. The symbols a

_{c}and b

_{c}are the fitting coefficients of the CCD camera, respectively.

^{2}. The symbol $\rho}_{\mathrm{S}$ is the reflectivity of the left side surface of the rear target, and it is about 0.8. The symbol ${f}_{\mathrm{S}}$ is the transmittance of the neutral density filter installed at the CCD camera during the measurement. The symbol $G{V}_{\mathrm{S},\left(i,j\right)}$ is the gray value at pixel (i, j) of the image photographed by the CCD camera.

#### 2.2. Experimental Apparatus

^{2}.

_{c}and b

_{c}in Equation (1) are equal to 0.08778 and −0.6112, respectively.

## 3. MCRTM Method Coupled with Experimental CSRF on the Focal Plane

^{9}solar rays were sampled for each case. The flowchart of the MCRTM together with the measured results is shown in Figure 4, where the emission positions and the directions are determined by the measured relative CSRI. The symbol N

_{t}is the total ray number sampled, which is set to 10

^{9}as discussed.

## 4. Measurement Results and Experimental Verification

#### 4.1. Composite Measurement of the CSRF Density Distributions

^{2}, as shown in Figure 5.

^{2}. The relative error of the peak heat flux density between the direct and the indirect measurements is about 3.6%. Because the probe of the heat flux meter is too large compared to a single pixel on the curve, the value recorded by the heat flux meter represents the average gray value of the CCD graph inside the rectangular box.

^{6}W/m

^{2}, B = 2560 m

^{−2}.

#### 4.2. The Directional Characteristics of the CSRF

^{−5}to avoid the saturation of the CCD camera), as shown in Figure 6a.

^{2}. In the other three quadrants, the CSRF distributions are relatively uniformly and low. There is a blue hole in the central region, which means that the heat flux in this region is negligible.

#### 4.3. Influences of the Directional CSRI on Thermal Conditions of the Cavity Receiver

^{2}to 0.1 MW/m

^{2}. The relative error of the CSRF value in Figure 7b and that in Figure 7c is up to 16%. These values prove that the directional CSRI plays an important role in the CSRF images of the cavity receiver. More accurate thermal conditions of solar receivers can be obtained when both the spatial CSRF and the directional CSRI are measured together. It is beneficial to the heat transfer improvement of solar thermal applications.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

a_{c},b_{c} | fitting coefficients of the CCD camera |

GV | gray value of the CCD camera |

f_{s} | transmittance of the neutral density filter |

h_{x} | size of the rear target surface along x axis |

h_{y} | size of the rear target surface along y axis |

I_{s} | concentrated solar radiative intensity(CSRI), W/(m^{2}·sr) |

${{I}^{\prime}}_{\mathrm{S}}$ | Relative CSRI, |

L_{S,(i,j)} | incoming solar radiant intensity of the rear target at grid (i, j), W/m^{2} |

l | spacing between the front and rear target, m |

N_{x} | pixel number of the rear target surface image along x axis |

N_{y} | pixel number of the rear target surface image along y axis |

q_{s} | spatial distribution of the CSRF, w/m^{2} |

x | x-direction coordinate, m |

y | y-direction coordinate, m |

r | emission radius for the solar ray, m |

r_{0} | radius of the CSRF spot, m |

R | correlation coefficient of the fitting functions |

R_{φ}, R_{r}, R_{β}, R_{θ} | random number uniformly distributed between zero and one |

Greek symbols | |

θ | zenith angle |

β | circumferential angle |

ΔA | area of surface element, m^{2} |

ΔΩ | solid angle of surface element, sr |

ΔA_{HM} | area of the horn mouth, m^{2} |

μ | total uncertainty |

μ_{A} | type A uncertainty |

μ_{B} | type B uncertainty |

ρ_{s} | reflectivity of the lambertian target |

Subscripts | |

s | solar radiation |

i, j | surface element |

0 | emission positon |

Abbreviations | |

CSRF | concentrated solar radiation flux |

CSRI | concentrated solar radiative intensity |

MCRTM | Monte-Carlo ray-tracing method |

CCD | Charge coupled Device |

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**MDPI and ACS Style**

Dai, G.; Zhuang, Y.; Wang, X.; Chen, X.; Sun, C.; Du, S.
Experimental Investigation on the Vector Characteristics of Concentrated Solar Radiation Flux Map. *Energies* **2023**, *16*, 136.
https://doi.org/10.3390/en16010136

**AMA Style**

Dai G, Zhuang Y, Wang X, Chen X, Sun C, Du S.
Experimental Investigation on the Vector Characteristics of Concentrated Solar Radiation Flux Map. *Energies*. 2023; 16(1):136.
https://doi.org/10.3390/en16010136

**Chicago/Turabian Style**

Dai, Guilong, Ying Zhuang, Xiaoyu Wang, Xue Chen, Chuang Sun, and Shenghua Du.
2023. "Experimental Investigation on the Vector Characteristics of Concentrated Solar Radiation Flux Map" *Energies* 16, no. 1: 136.
https://doi.org/10.3390/en16010136